International Journal of Electronics andCommunications (AEÜ)
j our na l ho mepage: www.elsev ier .de /a eue
valuating the effects of node cooperation on DTN routing
ong Li ∗, Guolong Su, Zhaocheng Wangtate Key Laboratory on Microwave and Digital Communications, Tsinghua National Laboratory for Information Science and Technology,epartment of Electronic Engineering, Tsinghua University, Beijing 100084, China
r t i c l e i n f o
rticle history:eceived 4 May 2010ccepted 6 May 2011
Due to the uncertainty of transmission opportunities between mobile nodes, delay tolerant networks(DTN) routing exploits the opportunistic forwarding mechanism. This mechanism requires nodes toforward messages in a cooperative way. However, in the real word, most of the nodes exhibit non-cooperation behaviors such as dropping and not relaying messages. In this letter, we investigate theproblem of how the non-cooperation behaviors of nodes influence the performance of DTN routingalgorithms of two-hop relay and epidemic routing. First, we model the message delivery process with non-cooperation behaviors by a two dimensional continuous time Markov chain. Then, we obtain the system
performance of message delivery delay and delivery cost by explicit expressions. Numerical results showthat different non-cooperation behaviors may have opposite impacts on different routing algorithms.Specifically, dropping message increases the message delivery delay and delivery cost in the two-hoprelay, while increases the delay but does not affect the delivery cost in the epidemic routing, and notrelaying message increases the delivery delay but decreases the delivery cost for both the two-hop and epidemic routing.
. Introduction
In order to provide communication services in the highly chal-enged wireless networks that have only intermittent connectivity,uch as vehicular ad hoc networks for road safety and commer-ial applications [1], sparse sensor networks for wildlife trackingnd habitat monitoring [2], deep-space interplanetary networks [3]nd mobile social networks [4], delay tolerant networks (DTN) [2]ere proposed. In DTN, there are no end-to-end paths between
he communication source and destination [5]. For example, inhe vehicular DTN, the nodes are vehicles and they move veryuickly. Therefore, the network is highly mobile and frequentlyisconnected, and it is unrealistic to maintain end-to-end pathsetween any communication source and destination pairs. There-ore, its routing algorithms are quite different from the Internet andraditional ad hoc networks. The new mechanism for DTN routings called store-carry-and-forward [2,5], which exploits the oppor-unistic contacts between nodes and mobility to relay and carry
essages. In store-carry-and-forward routing, if the next hop is notmmediately available for the current node to forward a message,he node will store the message in its buffer, carry it along while
oving, and forward it to other appropriate nodes until the nodeets a communication opportunity which helps to forward thisessage farther. Therefore, the nodes must be capable of buffer-
ing messages for a considerable time. Moreover, to increase theprobability of delivery, the messages will be replicated many timesin the network due to the lack of complete information about othernodes. For example, in Epidemic routing [6], packets arriving at theintermediate nodes are forwarded to all of their neighbors.
Obviously, this new routing mechanism requires the nodes toforward messages in a cooperative and selfless way [7]. For exam-ple, every node should utilize its own limited buffer to store themessage, carry the message along the movement, and forward themessage when it contacts with others to helps to deliver this mes-sage. Otherwise, most of the messages would not be transmittedto the destination successfully. However, in real world, most ofthe nodes exhibit non-cooperative behaviors [8], which would notstore messages in their buffer, or even not relaying messages forothers in order to conserve the limited buffer and power resources.To the best of our knowledge, only a few existing works [9,10]deal with node cooperation issues in DTN. A. Panagakis et al. in[9] evaluate the DTN routing performance under different levels ofcooperation through simulation. At the same time, G. Resta and P.Santi in [10] present a theoretical framework to study the effectsof different degrees of node cooperation. However, the proposedframework can only derive the performance of message deliverydelay and is not able to study the tradeoff between the deliverydelay and cost caused by the non-cooperation behaviors.
In this letter, we focus on the performance evaluation and thetradeoff analysis by considering the non-cooperation behavior ofnodes, which is characterized by the probability for nodes not toreceive messages and the probability to drop messages. We con-
ider two typical routing algorithms, two-hop relay and epidemicouting. By modeling the message dissemination process amonghe non-cooperation nodes as a two-dimensional continuous time
arkov chain, we derive the system performance of message deliv-ry delay and delivery cost. Then, we study the performance andhe tradeoff by extensive numerical results. They demonstrate thathe non-cooperation behaviors deteriorate the message deliveryelay for both the two-hop relay and epidemic routing, and dif-erent non-cooperation behaviors may have opposite impacts onhe message delivery cost. Related to different routing schemes,e show that the node cooperation plays a more important role in
he performance of epidemic routing than that of two-hop relay.The outline of this letter is as follows: In Section 2, we present the
ystem model and analysis the performance of message deliveryelay and delivery cost. In Section 3, we give the parameter settingsnd analyze the numerical results. Finally, Section 4 concludes theetter.
. System model and performance analysis
.1. System model
We model a DTN as a set of wireless mobile nodes, and theumber of nodes is assumed to be N + 1. Among them, there are
source node and a destination node. In this work, we considerne message transmission from the source to the destination, andnvestigate the performance of message delivery delay and cost.ince the density of the nodes is sparse in DTN environment, theyan communicate only when they move into the transmission rangef each other, which means a communication contact. We assumehe occurrence of the contacts between two nodes follows Poissonistribution, which is used by [4]. We use � to denote the contactccurrence rate. Consequently, the inter-contact time between twoodes follows exponential distribution. This assumption is demon-trated to hold by works of [11,12], which model the inter-contactime of real mobility traces from vehicles. Upon a contact that mayesult in message transmission, the node non-cooperation behav-ors would take effect. In this work, we consider two types ofode non-cooperation behavior: probability reception and drop-ing. That means the node may not be cooperative in the messageelivery by choosing not to receive the message or receive and thenrop it. In the system we study, we assume that upon reception ofhe message for a node, it receives the message with probability pf,nd then discards the message with probability pd or keeps it andollows the rules of the routing algorithm with probability (1 − pd).onsequently, the probability of pf and (1 − pd) can be referred toooperation levels.
For the DTN routing schemes, we investigate two typical rout-ng algorithms, two-hop relay and epidemic routing. In the two-hopelay, the transmission has two hops between the source and des-ination. It is a basically simple routing scheme of DTN. Epidemicouting is a kind of flooding-based scheme since it tries to sendach message over all possible paths in the network. This provides
large amount of redundancy because all nodes receive every mes-age. Since it tries every possible path, it delivers messages with theinimum delivery delay and maximum delivery ratio. It is partic-
larly useful for theoretical purposes since its delivery ratio andelivery delay is also that of the optimal single-copy time spaceouting protocol. Therefore, in this paper, we choose to study thechemes of two-hop relay and epidemic routing. Considering theessage routing process under the node non-cooperation behav-
ors, we can model it by a two-dimensional continuous time Markovhain with state (n(t), x(t))t≥0, where n(t) represents the number ofodes that have received the message, and x(t) represents the num-er of nodes that have a copy of the message in their buffer, at time
Fig. 1. The continuous time Markov chain for modeling the message disseminationprocess with node cooperation. States (1,1) to (N, 1) are (N(N + 1))/2 transient statesand state (D) is the absorbing state.
t. Thus, n(t) represents the times of message transmissions, and x(t)is related to the successful transmission probability. Therefore, wecan obtain that this Markov chain starts with state (1, 1), and hasS = (N(N + 1))/2 transient states. In any transient state (n(t), x(t)),the message may be forwarded to the destination, which meansthe absorbing state, denoted by state (D). Consequently, the num-ber of total states is S + 1. In every transient state of this Markovchain, the system will remain in the current state for exponentiallydistributed amount of time and then transit to another differentstate. This process is characterized by “transition rate” betweenthese two states, which measures how quickly the state transitionhappens. According to the state transition diagram shown in Fig. 1,we can obtain its generator matrix Q with dimension of S + 1 as thefollowing form:
Q =(
T R0 0
), (1)
where sub-matrix T is a S × S matrix with element Ti,j meaning thetransition rate from transient state (i) to state (j), R is aS × 1 matrixwith element Ri,D meaning the transition rate from transient state(i) to the absorbing state (D). The left 0 matrix is a 1 × S vector withall element 0 meaning the zero transition rates from the absorbingstate to transient states. The right 0 matrix degenerates to a sin-gle 0 element representing the negative sum of the left 0 vector.According to the different routing algorithms controlling the mes-sage forwarding, we can obtain the transition rate {qi,j} from thestate i to state j as the following two subsections.
2.1.1. Two-hop relay routingIn the two-hop forwarding, the source node can replicate the
message to any other nodes, but the other nodes can only forwardit to the destination. The two-hop relay aims at limiting the num-ber of message transmissions. Therefore, the time for the messageto reach the destination is usually very long. Although the messagedelivery delay is very large, the destination will be reachable bymore and more relay nodes having received the message from thesource. We consider the message transmission process when thesystem is in the transient state (n, x). There are x nodes with themessage, n − x nodes have dropped the message and N − n nodeswithout the message. When one of the nodes without the message
encounters the source, if it chooses to receive and then discard themessage, the system state turns to (n + 1, x), and if it does not dropthe message, the system state turns to (n + 1, x + 1). According tothe cooperation rules we defined, we can obtain the transition rate
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4 Y. Li et al. / Int. J. Electron. C
rom state (n, x) to state (n + 1, x) is �(N − n)pfpd because there are − n nodes can receive the message from the source without non-ooperation behaviors, the probability of which is pfpd, in the ratef �. Similarly, the transition rate from state (n, x) to state (n + 1,
+ 1) is �(N − n)pf(1 − pd). When one of the nodes with the mes-age encounters the destination, the system turns to state (D), andhe transition rate is x�. We use Tt and Rt to denote T and R respec-ively in Q defined in (1). Consequently Tt{(a, b) | (n, x)} denoteshe transition rate from state (n, x) to state (a, b) and Rt{(D) | (n, x)}enotes the transition rate from state (n, x) to absorbing state (D).herefore, the non-zero transition rates are given as following.
Tt{(n + 1, x + 1)|(n, x)} = �(N − n)pf (1 − pd), for n ∈ [1, N − 1]
Tt{(n + 1, x)|(n, x)} = �(N − n)pf pd, for n ∈ [1, N − 1], x ∈ [1, n
here Tt{(n, x) | (n, x)} is obtained since Tt{(n, x) | (n,)} = −
∑a,b;a /= n,b /= xTt{(a, b) | (n, x) + Rt{(D) | (n, x)}}, which is
he property of the generator matrix Q, and the transition ratesxcept Tt{(n + 1, x + 1) | (n, x)}, Tt{(n + 1, x) | (n, x)} and Rt{(D) | (n,)} are zero.
.1.2. Epidemic routingIn the epidemic routing, the message arriving at the intermedi-
te nodes is forwarded to all of the nodes’ neighbors in contact. Wean find that different from two-hop relay, in the epidemic rout-ng all nodes can forward the message to other nodes. Therefore,here are no constraints on the number of message copies in theetwork, and the message is transmitted in a flooding way. Finally,
t is transmitted to the destination by any of the nodes with theessage. Consider the system in state (n, x). The transition rate to
n + 1, x + 1) is x�(N − n)pf(1 − pd) since there are N − n nodes mayeceive the message in the rate of � with probability pf from x nodesnd with probability 1 − pd not to discard it. Similarly, the transi-ion rate to (n + 1, x) is x�(N − n)pfpd. We use Te and Re to denote Tnd R respectively in Q defined in (1). Consequently, Te{(a, b) | (n,)} denotes the transition rate from state (n, x) to state (a, b) ande{(D) | (n, x)} denotes the transition rate from state (n, x) to absorb-
ng state (D). Similar to the analysis in two-hop relay, we have theransition rates given by the following expressions.
Te{(n + 1, x + 1)|(n, x)} = x�(N − n)pf (1 − pd), for n ∈ [1, N − 1
Te{(n + 1, x)|(n, x)} = x�(N − n)pf pd, for n ∈ [1, N − 1], x ∈ [1,
here Te{(n, x) | (n, x)} is obtained by the same reason for the two-op relay, which is explained in Section 2.1.1.
.2. Performance analysis
Based on the Markov chain model, we consider two importantystem performance metrics, message delivery delay and messageelivery cost, which are defined as follows:
Message delivery delay: The average time consumed to deliver themessage to the destination.Message delivery cost: The average number of times that the mes-sage is transmitted until it has been forwarded to the destination.
n. (AEÜ) 66 (2012) 62– 67
[1, n];
)|(n, x)}, for n ∈ [1, N], x ∈ [1, n].
(2)
[1, n];
D)|(n, x)}, for n ∈ [1, N], x ∈ [1, n].
(3)
2.2.1. Message delivery delayAccording to the transition matrix Tt(e) and Ref. [13], we have
the message deliver delay, denoted by Dd, as follows:
Dd = e · (−T−1t(e)) · I, (4)
where e = [1, 0, . . ., 0] is a 1 × K vector denoting the initial stateprobability vector, and I = [1, 1, . . ., 1] is a 1 × K all-one vector.
2.2.2. Message delivery costTo get the message delivery cost, we should know the transition
probability from the transient state (i)i∈[1,S] to the absorbing state
(D). For this purpose, we consider the corresponding embeddedMarkov chain denoted by P. Its element pi,j is expressed as follows:
pi,j ={
−qi,j/qi,i, j /= i;0, j = i.
P means the single step transition probability matrix, and conse-quently, the transition probability from state (0, 0) to state (D),denoted by P1,S+1, is P1,S+1 = p1,S+1. P2 means the two step transi-tion probability matrix. Thus, the transition probability from state(1,0) and state (0, 1) to the state (D) is P2
1,S+1. Similarly, Pi meansi step transition probability matrix. Therefore, we obtain the mes-sage delivery cost, denoted by Dc as the following expression:
Dc =X+1∑i=1
i · Pi1,S+1. (5)
3. Numerical results
In this section, we give numerical results of message deliverydelay and delivery cost. We obtain the results by simulating thecontinuous-time system with Matlab®. The parameters in our eval-uation include the contact rate �, the number of nodes N, dropping
probability pd and receiving probability pf. Related to �, we use thesimilar approach in Ref. [14] to obtain, which considers a standardRandom Waypoint (RWP) mobility scenario. From Ref. [15], we canobtain that for RWP � = (8ωrv)/�L2, where ω = 1.3683 is a constant,r is the transmission range, v is the node’s scalar speed, and L is theplayground size. In the numerical simulation, the parameters areset as follows: � = 2.51 h−1 with r = 20 m, v = 10 m/s and L = 1000 m,and pd, pf and N are set as variable parameters for the investigation.We note that the cooperation level of nodes is proportional to pf andis inversely proportional to pd. In order to analyze the influence of
node cooperation behaviors conveniently, we define two metrics ofcooperation factor, denoted by Fd and Ff, as Fd = (1 − pd) and Ff = pf.Cooperation factor of Fd is related to the non-cooperation behaviorof discarding message, while Ff is related to the behavior of not
Y. Li et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 62– 67 65
10 20 30 40 500.05
0.1
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sage
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elay
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d)
pf=0.2, 0.5, 0.5, 0.5, 0.8, 1
pd=0.8, 0.8, 0.5, 0.2, 0.2, 0
(a)
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d) p
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pf=0.2, 0.5, 0.5, 0.5, 0.8, 1
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F(
fl
wrdScwCtsfFhtserf
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wpsdmirot
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ly E
nhan
cem
ent R
atio
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dr )
pd=0.5, p
f=0.5
pd=0.2, p
f=0.5
pd=0.0, p
f=0.1
Epidemic
Two−hop
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atio
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dr )p
f=1 p
f=0.8 p
f=0.6 p
f=0.4
Two−hop
Epidemic
(b)
Fig. 3. Enhanced ratio of delivery delay with different cooperation factor of both
orwarding message. Now, we have that the nodes’ cooperationevel is proportional to both Fd and Ff.
Fig. 2(a) and (b) shows the results of message delivery delayith different pd and pf in the two-hop relay and epidemic routing,
espectively. From the results, we can observe that the deliveryelay decreases with the increasing of the number of nodes N.ince the increasing in the number of nodes means more nodesan help to relay and forward the message to the destinations, itill create more transmission opportunities to deliver the message.onsequently, the message will be transmitted from the sourceo the destination more quickly. This results in the reduced mes-age delivery delay. When we increase the cooperation factorsFdrom 0.2 to 0.8 by decreasingpd from 0.8 to 0.2 and increasef from 0.2 to 1, the delivery delay decreases in both the two-op relay and epidemic routing. On the other hand, we obtainhat the non-cooperation behaviors of nodes will deteriorate theystem performance of delivery delay. In order to evaluate thenhancement ratio of different cooperation factor, we define aelated metric of delay enhancement ratio, denoted by Dr
d, as
ollows:
rd = Dd(0.8, 0.2) − Dd(pd, pf )
Dd(0.8, 0.2), (6)
here Dd(0.8, 0.2) is the message delivery delay when pd = 0.8 andf = 0.2. Since the most non-cooperation behavior in our simulationetting is pd = 0.8 and pf = 0.2, which provides the largest messageelivery delay, we use Dd(0.8, 0.2) as the baseline to evaluate howuch performance enhancement we can obtain if nodes behav-
or more cooperative. We plot the results of delay enhancementatio for two-hop relay and epidemic routing in Fig. 3(a). We canbserve that the larger the cooperation factor Fd or Ff, the largerhe enhancement ratio Dr
d. When we set pd to 0.8 and change pf,
two-hop relay and epidemic routing. (a) With variable pf and pd and (b) with variablepf and fixed pd = 0.8.
the same results can be observed in Fig. 3(b). Related to differentrouting algorithms, Dr
dof two-hop is always smaller than that of epi-
demic routing when the cooperation factor is the same. That is tosay, the epidemic routing will have more performance gain in termsof delivery delay than two-hop relay when nodes are more coopera-tive in the network. On the other hand, we can obtain that two-hoprelay is more robust to non-cooperation behaviors of nodes thanepidemic routing.
Fig. 4 shows the results of message delivery cost with differentpd and pf in the two-hop relay. From the results, we can obtain thatthe delivery cost increases with the increasing of N. To study theimpacts of different cooperation Fd, we study the effects of pd andpf separately in Fig. 4 (a) and (b), respectively. We can observe thatwhen we set Fd = 0.2 and decrease Ff from 1.0 to 0.2, the deliverycost is reduced, while we set Ff = 0.2 and decrease Fd from 1.0 to0.2 by increasing pd from 0 to 0.8, the delivery cost is increased.This reveals that the cooperation factors Ff and Fd have differentimpact on the delivery cost in the two-hop relay. More specifically,the decreasing of Ff caused by the non-cooperation behavior of notreceiving message decreases the delivery cost while the decreas-ing of Fd caused by the behavior of dropping message increases thedelivery cost. Related to the epidemic routing, we can obtain that Fddoes not influence the delivery cost because the transition proba-bility pi,j is not a function of the number of nodes with the message.Therefore, if some nodes choose to drop message, it only affects thedelivery cost. Therefore, we set pd = 0.8 and plot the results in Fig.5(a). Similar to two-hop relay, we can obtain that the larger theF , the larger the delivery cost. Therefore, we come to the conclu-
fsion that the non-cooperation behavior of not receiving messagealthough increases the message delivery delay, there is a gain ofdecreasing the delivery cost.
66 Y. Li et al. / Int. J. Electron. Commu
5 10 15 20
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ost (
DC) p
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sage
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iver
y C
ost (
DC
) pd=0.0
pd=0.2
pd=0.4
pd=0.6
pd=0.8
(b)
Fig. 4. Simulation results of message delivery cost for two-hop relay. (a) Withpd = 0.8 and (b) with pf = 0.2.
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t Deg
ener
atio
n R
atio
(D
cr )
pf=1 p
f=0.8 p
f=0.6 p
f=0.4
Epidemic
Two−hop
(b)
Fig. 5. Simulation results of message delivery cost. (a) Epidemic routing with pd = 0.8and (b) degeneration ratio of delivery cost for two-hop and epidemic with pd = 0.8.
[
[
n. (AEÜ) 66 (2012) 62– 67
Similar to the analysis of delivery delay, to investigate theimpact of pf on the delivery cost, we define a metric of cost increaseratio, denoted by Dr
c , as follows:
Drc = Dc(0.8, pf ) − Dc(0.8, 0.2)
Dc(0.8, 0.2), (7)
where Dc(0.8, 0.2) is the message delivery cost when pf = 0.2 andpd = 0.8. Similar to delay enhancement ratio defined in (6), we useDc(0.8, 0.2) as the baseline, which achieves the least message deliv-ery cost, to evaluate how much the cost will increase if nodesforward the message with a higher probability. The results areshown in Fig. 5(b). We can observe that with the increasing of Ff,the increase ratio becomes larger, and the ratio of epidemic rout-ing is always larger than two-hop relay. Comparing Fig. 3(b) and5(b), we can obtain that the reduced delay ratio is much smallerthan the increased cost ratio when the nodes behave more coop-erative in the message delivery. On the other hand, we derive thatDTN is quite robust to non-cooperation behavior of not receivingmessage, which increases the message delivery delay, but there ismore reducing of delivery cost.
4. Conclusion
In this letter, we investigate the performance of the two-hop relay and epidemic routing in the delay tolerant networkswith non-cooperation behaviors in message delivery by focusingon the message delivery delay and delivery cost. By numericalresults, we show that the nodes’ non-cooperation behaviors ofboth dropping and not receiving message deteriorate the systemperformance of message delivery delay. Related to the messagedelivery cost, the behavior of dropping message increases the costin the two-hop relay, while the behavior of not receiving messagereduces the cost. Furthermore, we reveal that the two-hop relayis more robust to non-cooperation behaviors than the epidemicrouting.
Acknowledgements
This work is supported by National Major Scientific andTechnological Specialized Project (No. 2010ZX03004-002-02),National Basic Research Program (No. 2007CB310701), PCSIRT andTNLIST.
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